Below are listed rank-two temperaments supported by the 24edo patent val, below the indicated cutoff in TE badness.

7-limit temperaments with badness below 0.06

Listed is the wedgie and the TE badness times 1000 for six temperaments with badness less than 0.06.

Rank	Wedgie	Name	Badness	Commas
1	<<2 8 1 8 -4 -20]]	Godzilla	26.747	49/48 81/80
2	<<2 -16 25 -30 34 103]]	Hemischis	45.817	6144/6125 19683/19600
3	<<4 -8 14 -22 11 55]]	Shrutar	47.377	245/243 2048/2025
4	<<0 0 12 0 19 28]]	Catler	50.297	81/80 128/125
5	<<6 0 3 -14 -12 7]]	Triforce	54.988	49/48 128/125
6	<<2 8 -11 8 -23 -48]]	Mohajira	55.714	81/80 6144/6125

11-limit temperaments with badness below 0.05

Listed is the wedgie and the TE badness times 1000 for 17 temperaments with badness less than 0.05.

Rank	Wedgie	Name	Badness	Commas
1	<<2 8 -11 5 8 -23 1 -48 -16 52]]	Mohajira	26.064	81/80 121/120 176/175
2	<<6 0 3 3 -14 -12 -16 7 7 -2]]	Triforce	26.152	49/48 56/55 77/75
3	<<4 -8 14 -2 -22 11 -17 55 23 -54]]	Shrutar	26.489	121/120 176/175 245/243
4	<<0 0 12 12 0 19 19 28 28 -8]]	Catcall	34.478	56/55 81/80 128/125
5	<<2 8 1 -7 8 -4 -18 -20 -44 -23]]	Baragon	35.673	49/48 56/55 81/80
6	<<2 8 13 5 8 15 1 8 -16 -31]]	Mohamaq	36.207	56/55 77/75 243/242
7	<<0 24 -24 0 38 -38 0 -123 -83 83]]	Hours	36.248	243/242 385/384 9801/9800
8	<<4 -32 38 -2 -60 49 -17 178 106 -137]]	Kleischismic	36.749	385/384 9801/9800 14641/14580
9	<<6 0 15 15 -14 7 3 35 35 -10]]	Hemiaug	38.232	56/55 128/125 245/243
10	<<2 -16 13 5 -30 15 1 75 67 -31]]	Salsa	39.444	243/242 245/242 385/384
11	<<2 8 1 17 8 -4 20 -20 12 44]]	Varan	39.647	49/48 77/75 81/80
12	<<4 -8 26 10 -22 30 2 83 51 -62]]	Sruti	41.459	176/175 243/242 896/891
13	<<4 16 2 10 16 -8 2 -40 -32 21]]		42.259	49/48 81/80 121/120
14	<<8 -64 88 8 -120 117 -15 384 240 -282]]		44.778	9801/9800 32805/32768 46656/46585
15	<<8 8 16 8 -6 3 -15 15 -9 -33]]	Semidim	47.598	56/55 77/75 245/243
16	<<8 -40 64 8 -82 79 -15 261 157 -199]]		48.007	6144/6125 9801/9800 19712/19683
17	<<4 -8 2 10 -22 -8 2 27 51 21]]	Anguirus	49.253	49/48 56/55 243/242